How to get an AUC confidence interval

Background

AUC is an important metric in machine learning for classification. It is often used as a measure of a model’s performance. In effect, AUC is a measure between 0 and 1 of a model’s performance that rank-orders predictions from a model. For a detailed explanation of AUC, see this link.

Since AUC is widely used, being able to get a confidence interval around this metric is valuable to both better demonstrate a model’s performance, as well as to better compare two or more models. For example, if model A has an AUC higher than model B, but the 95% confidence interval around each AUC value overlaps, then the models may not be statistically different in performance. We can get a confidence interval around AUC using R’s pROC package, which uses bootstrapping to calculate the interval.

Building a simple model to test

To demonstrate how to get an AUC confidence interval, let’s build a model using a movies dataset from Kaggle (you can get the data here).

Reading in the data

# load packages
library(pROC)
library(dplyr)
library(randomForest)

# read in dataset
movies <- read.csv("movie_metadata.csv")

# remove records with missing budget / gross data
movies <- movies %>% filter(!is.na(budget) & !is.na(gross))

Split into train / test

Next, let’s randomly select 70% of the records to be in the training set and leave the rest for testing.

# get random sample of rows
set.seed(0)
train_rows <- sample(1:nrow(movies), .7 * nrow(movies))

# split data into train / test
train_data <- movies[train_rows,]
test_data <- movies[-train_rows,]

# select only fields we need
train_need <- train_data %>% select(gross, duration, director_facebook_likes, budget, imdb_score, content_rating, movie_title)
test_need <- test_data %>% select(gross, duration, director_facebook_likes, budget, imdb_score, content_rating, movie_title)

Create the label

Lastly, we need to create our label i.e. what we’re trying to predict. Here, we’re going to predict if a movie’s gross beats its budget (1 if so, 0 if not).

train_need$beat_budget <- as.factor(ifelse(train_need$gross > train_need$budget, 1, 0))
test_need$beat_budget <- as.factor(ifelse(test_need$gross > test_need$budget, 1, 0))

Train a random forest

Now, let’s train a simple random forest model with just 50 trees.

train_need <- train_need[complete.cases(train_need),]

# train a random forest
forest <- randomForest(beat_budget ~ duration + director_facebook_likes + budget + imdb_score + content_rating,
                       train_need, ntree = 50)

Getting an AUC confidence interval

Next, let’s use our model to get predictions on the test set.

test_pred <- predict(forest, test_need, type = "prob")[,2]

And now, we’re reading to get our confidence interval! We can do that in just one line of code using the ci.auc function from pROC. By default, this function uses 2000 bootstraps to calculate a 95% confidence interval. This means our 95% confidence interval for the AUC on the test set is between 0.6198 and 0.6822, as can be seen below.

ci.auc(test_need$beat_budget, test_pred) 
# 95% CI: 0.6198-0.6822 (DeLong)

We can adjust the confidence interval using the conf.level parameter:

ci.auc(test_need$beat_budget, test_pred, conf.level = 0.9) 
# 90% CI: 0.6248-0.6772 (DeLong)

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See here to learn more about the pROC package.